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Chinese Annals of Mathematics, Series B

, Volume 37, Issue 5, pp 665–682 | Cite as

The cauchy problem for coupled nonlinear Schrödinger equations with linear damping: Local and global existence and blowup of solutions

  • João-Paulo Dias
  • Mário Figueira
  • Vladimir V. Konotop
Article
  • 44 Downloads

Abstract

The authors study, by applying and extending the methods developed by Cazenave (2003), Dias and Figueira (2014), Dias et al. (2014), Glassey (1994–1997), Kato (1987), Ohta and Todorova (2009) and Tsutsumi (1984), the Cauchy problem for a damped coupled system of nonlinear Schrödinger equations and they obtain new results on the local and global existence of H 1-strong solutions and on their possible blowup in the supercritical case and in a special situation, in the critical or supercritical cases.

Keywords

Nonlinear Schrödinger equations Cauchy problem Blowup of solutions Dissipation 

2000 MR Subject Classification

35Q55 33A05 

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Copyright information

© Fudan University and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • João-Paulo Dias
    • 1
  • Mário Figueira
    • 1
  • Vladimir V. Konotop
    • 2
  1. 1.CMAF-CIO, Faculdade de CiênciasUniversidade de LisboaLisboaPortugal
  2. 2.Centro de Física Teórica e Computacional and Departamento de Física, Faculdade de CiênciasUniversidade de LisboaLisboaPortugal

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